The multiplayer files have most of the game content files. The singleplayer download only downloads the singleplayer exclusive content, and it reads the rest of teh content from the multiplayer folder, meaning that downloading just singleplayer isn't downloading the entire game.

You should be able to do the campaign without DL the MP unless you want to play Zombies. Or at least I can. I just tried it.

I never tried only SP or MP in cod games before WW2, but it works. Try this way:
DL the game to the hardisc you wanted them to be located on. Then uninstall the one you don't want. Next - you verify integrety for locale files in steam library. For me: First verifying only DL the shared files. Next verifying (with about 50 MB DL) - steam install the files.
Now the game worked. I tried both SP and MP.
Do the same if you split the SP and MP on different disc's.

How to play the campaign???
It wont allow me to I only have multiplayer wtf help